# 852HW10 - HOMEWORK ASSIGNMENT 10 PHYS852 Quantum Mechanics II Spring 2009 New topics covered partial waves scattering resonances 1 Hard-sphere

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: HOMEWORK ASSIGNMENT 10 PHYS852 Quantum Mechanics II, Spring 2009 New topics covered: partial waves, scattering resonances . 1. Hard-sphere S-wave scattering: Consider S-wave scattering from a hard sphere of radius a . Make the ansatz ψ ( r,θ,φ ) = e- ikr r- (1 + 2 ikf ( k )) e ikr r and show that it is an eigenstate of the full Hamiltonian for all r > a . Fit the value of f ( k ) to satisfy the boundary condition ψ ( a,θ,φ ) = 0. What is the partial amplitde f ( k )? What is the s-wave phase-shift δ ( k )? 2. Hard-sphere P-wave scattering: For P-wave scattering from a hard sphere of radius a , make the ansatz ψ ( r,θ ) = bracketleftbiggparenleftbigg 1 kr- i ( kr ) 2 parenrightbigg e- ikr + (1 + 2 ikf 1 ( k )) parenleftbigg 1 kr + i ( kr ) 2 parenrightbigg e ikr bracketrightbigg Y 1 ( θ ) , and show that it is an eigenstate of the full Hamiltonian for r > a . Again solve for the partial amplitude f 1 ( k ) by imposing the boundary condition ψ ( a,θ ) = 0. What is the phase-shift) = 0....
View Full Document

## This note was uploaded on 10/25/2010 for the course PHYSICS PHYS 851 taught by Professor Michaelmoore during the Fall '08 term at Michigan State University.

Ask a homework question - tutors are online